Process for determining the relative velocity between two moving objects

ABSTRACT

The invention relates to a process for determining the relative velocity in the radial direction between two moving objects, using linear frequency modulation with continuous frequency sweeps. A problem in such processes lies in being clearly able. to determine the phase difference. According to the invention, a clear determination is realized by varying the period. length for successive frequency sweeps and using the difference in period length and corresponding phase change in determining the volocity.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a process for determining the relativevelocity in the radial direction between two moving objects, usinglinear frequency modulation with continuous frequency sweeps, atransmitted signal being multiplied by a received signal for theattainment of a resultant received signal, the phase change of whichover a certain time is used to determine the relative velocity.

2. Description of Related Art

A problem in determining the velocity where linear frequency modulationis used is to be able clearly to determine the phase difference. Thephase change is normally only known at ±n·2π, where n is a positiveinteger.

SUMMARY OF THE INVENTION

The object of the present invention is to realize a process in which thephase difference can clearly be determined. The object of the inventionis achieved by a process characterized in that the period length forsuccessive frequency sweeps is varied and in that the difference inperiod length and corresponding phase change is used to determine thevelocity. By studying the phase change over a time period which can bemade significantly shorter than the period length for a frequency sweep,the phase change can be kept within a clear interval.

The relative velocity v is advantageously calculated from therelationship:

v=k·x/ΔT,

where x is the phase difference during the time ΔT and${k = \frac{{c/2}\quad \pi}{{2\quad \alpha \quad t_{c}} + {2f_{0}}}},\quad {where}$

c denotes the velocity of the light in air, α denotes the gradient ofthe frequency sweep, t_(c) denotes the clock time and f₀ denotes thecarrier frequency of the signal.

The period length from a first to a second frequency sweep is changed byan amount less than or equal to the time difference which is required tobe able clearly to determine the phase change on the basis of givenlimit values for distance apart, velocity and acceleration.

At least three successive frequency sweeps are expediently assigned adifferent period length.

In order to increase the accuracy in the velocity determination, thetime interval during which the phase change is studied is progressivelyincreased without any loss of clarity. An advantageous process ischaracterized in that phase changes, over and above for differences inperiod lengths, are studied for one or more period lengths and/or one ormore added period lengths.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention shall be described in greater detail below with referenceto appended drawings, in which:

FIG. 1 shows examples of an emitted and a received signal in the case oflinear frequency modulation.

FIG. 2 shows examples of frequency sweeps of constant period length.

FIG. 3 shows examples of frequency sweeps according to the invention ofvarying period length.

FIG. 4 shows a diagrammatic example of a FMCW radar device, which can beused in the process according to the invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

Firstly, an account is given below of the theory behind linear frequencymodulation. The discussion then moves on to linear frequency modulationwith continuous frequency sweeps, so-called “linear FMCW”.

In linear frequency modulation, a signal is ideally transmitted at thefrequency f_(t)(t):

f _(t)(t)=f ₀ +αt, t≧0,

where α denotes the gradient of the frequency sweep and f₀ the carrierfrequency of the signal.

For an emitted frequency sweep, the argument Φ(t) for the transmittedsignal can be written:

Φ(t)=2π₀∫^(t) f _(r)(ξ)dξ=Φ(0)+2π[f ₀ ^(t)+{fraction (1/2 )}αt ²]

In the time domain, the transmitted signal is:

α(t)=α₀ sin[Φ(0)+2π(f ₀ ^(t)+½αt ²)]

The transmitted signal is reflected and received after the time τ andcan be written:

b(t)=b ₀ sin[Φ(0)+2π(f ₀(t−τ)+½α(t−τ)²)].t≧τ

The emitted signal has been denoted by 1 and the received by 2 in FIG.1, which shows the frequency f as a function of the time t. The transittime from the transmitter to the receiver is represented by τ.

If the transmitted signal and the received signal are multiplied,sorting out the high frequency sub-signal, the resulting signal will, byapplying Euler's formula for exponential functions, be:

c(t)=c ₀ cos[2π(f ₀ τ+αtτ−½ατ²)], t>τ

In the case of linear FMCW modulation, the sweep is allowed to proceedfor a certain time, after which the procedure is repeated. FIG. 2 showsexamples of linear FMCW modulation with frequency sweeps of constantperiod length. An emitted sweep is shown by an unbroken line, whilst areturn sweep has been shown by a dotted line. The frequency sweeps havebeen numbered with the index i.

The instant of each sweep is denoted by t and is regarded as local, witht=0 for the start of each frequency sweep. The actual instant which isglobal is denoted by T. An object or target in the radial direction atthe instant t of the frequency sweep and in respect of frequency sweepi, with the velocity v and the constant acceleration α parallel to thedirection of the signal, is parametrized according to:

r(t)=r _(i) +vt+½αt ²

r _(i) =r(0)

applicable where i is fixed.

This gives:

τ_(i)+2r _(i) /c+2vt/c+αt ² /c,

where c is the velocity of the light in the medium (air).

The resultant received signal, substituted by τ_(i), can be written:${{c_{i}(t)} = {c_{0}\quad {\cos \quad\left\lbrack {2\quad {\pi \quad\left\lbrack {\frac{2\quad \alpha \quad r_{i}{t\left( {1 - \frac{2v}{c} - \frac{\alpha \quad t}{c}} \right)}}{c} + \frac{f_{0}{t\left( {{2v} + {\alpha \quad t}} \right)}}{c} + \frac{2\quad \alpha \quad v\quad {t^{2}\left( {1 - \frac{v}{c}} \right)}}{c} + \frac{2\quad \alpha \quad \alpha \quad {t^{3}\left( {1 - \frac{2v}{c} - \frac{\alpha \quad t}{2c}} \right)}}{c} + \frac{2{r_{i}\left( {f_{0} - \frac{\alpha \quad r_{i}}{c}} \right)}}{c}} \right\rbrack}} \right\rbrack}}},\quad {t \geq r}$

The frequency for a received sweep i, f_(i), for the resultant receivedsignal, can be written:${f_{i}(t)} = {{\frac{}{t}\quad \left( {\frac{2\quad \alpha \quad r_{i}{t\left( {1 - \frac{2v}{c} - \frac{\alpha \quad t}{c}} \right)}}{c} + \frac{f_{0}{t\left( {{2v} + {\alpha \quad t}} \right)}}{c} + \frac{2\quad \alpha \quad v\quad {t^{2}\left( {1 - \frac{v}{c}} \right)}}{c} + \frac{2\quad \alpha \quad \alpha \quad {t^{3}\left( {1 - \frac{2v}{c} - \frac{\alpha \quad t}{2c}} \right)}}{c}} \right)} = {\frac{1}{c}\left\lbrack {{2\quad \alpha \quad {r_{i}\left( {1 - \frac{2v}{c}} \right)}} + {2v\quad f_{0}} - {\left( {\frac{4\quad \alpha \quad r_{i}\alpha}{c} + {2f_{0}} + {4\quad \alpha \quad v\quad \left( {1 - \frac{v}{c}} \right)}} \right)t} + {6\quad \alpha \quad {\alpha \left( {1 - \frac{2v}{c}} \right)}\quad t^{2}} - {\frac{8\quad \alpha \quad \alpha^{2}}{2c}t^{3}}} \right\rbrack}}$

For small values of t, consideration being given to incorporated terms,the expression of the frequency f_(i) can be simplified withoutdeviating substantially from the actual frequency. The followingsimplified expression of the frequency can be drawn up:

f _(i)(t)=l/c[2αr _(i)+2vf ₀+4αvt].

We further note that (ar_(i)/c)/f₀ has a small value, therebylegitimately enabling the resultant received signal to be simplified to:

c _(i)(t)=c ₀ cos[2π[2αr _(i) t/c+f ₀ t2v/c+2αvf−/c+2r ₁ f ₀ /c]], t≧τ

After a certain clock time t_(c), see FIG. 1, a first of a plurality ofsamples is taken of the signal. The argument Θ_(i) for the resultantreceived signal is referred to as the phase and can be written:

Θ_(i)=2π[2αr _(i) t _(c) /c+f ₀ t _(c)2v/c+2αvt _(c) ² /c+2r _(i) f ₀/c]

If the phase difference between two sweeps i, j is taken, the followingis obtained:

Θ_(j)−Θ_(i)=2π(2αt _(c) /c+2f ₀ /c)(r _(j) −r _(i))

The mean velocity between the instants T_(i) and T_(j) can then beexpressed according to the following:

v=(r _(j) −r _(i))/(T _(j) −T _(i))=(Θ_(j)−Θ_(i))i(T _(j) −T_(i))·(c/2π)/(2αt _(c)+2f ₀)

A description is provided below of a process according to the invention,using successive frequency sweeps having different period length,reference being made to FIG. 3.

The aim is to obtain an accurate determination of the velocity v for aninstant T. A good approximation of the velocity v is obtained by,according to the invention, instead determining the mean velocity over aperiod of time during which the velocity can be considered essentiallyconstant on the basis of limited acceleration.

FIG. 3 illustrates five emitted consecutive FMCW sweeps 1.1-1.5 havingdifferent period lengths and the associated return sweeps 2.1-2.5. For adetected object, FFT (Fast Fourier Transform) is taken for fiveconsecutive FMCW sweeps and five adjacent bearings. For these five FFTs,a frequency slot is designated in which the absolute value in the FFT isconsidered greatest. For this frequency slot, the respective phase valueΨ_(i) is also taken, which is an approximation to Θ_(i).

From the FFT, five phase values are obtained:

Ψ₁,Ψ₂, . . . Ψ₅,−π≦Ψ_(i)≦π,1≦i≦5

corresponding to the instants

T_(1, T) _(2, . . . T) ₅

The phase difference between two adjacent points then becomes:

ΔΨ₁ = (Ψ₂ − Ψ₁)_(mod 2π) ΔT₁ = T₂ − T₁ ΔΨ₂ = (Ψ₃ − Ψ₂)_(mod 2π) ΔT₂ = T₃− T₂ ΔΨ₃ = (Ψ₄ − Ψ₃)_(mod 2π) ΔT₃ = T₄ − T₃ ΔΨ₄ = (Ψ₅ − Ψ₄)_(mod 2π) ΔT₄= T₅ − T₄

where mod 2π denotes the modulo calculation over the interval [−π. π]⁻⁼.

The time differences ΔTi, 1≦i≦4 correspond to four PRI times (PulseRepetition Interval). The time for a FMCW sweep can be, for example, 370μs, the smallest PRI time being able to measure about 500 μs. In orderto be able clearly to determine a phase difference under prevailingconditions, a corresponding time difference of no more than about 10 μsis required. This task is managed according to the invention by using aplurality of different PRI times and then taking the difference betweenthese. In the numerical example, the smallest difference in PRI times is8 μs.

Any measuring errors on phase values over short time periods will have ahigh impact. In order to improve the precision in the velocitydetermination, the phase difference is measured over longer timeperiods, whilst, at the same time, care is taken to ensure that clarityis not lost. The PRI times are therefore chosen such that clarity iscombined with good precision in the velocity determination.

According to an example, the PRI times can have the following values:

ΔT₁=512 μs

ΔT₂=520 μs

ΔT₃=544 μs

ΔT₄=640 μs.

Inter alia, the following differences can herein be created:

ΔΔT₁ = ΔT₂ − ΔT₁   8 μs ΔΔT₂ = ΔT₃ − ΔT₁  32 μs ΔΔT₃ = ΔT₄ − ΔT₁  128 μsΔΔT₄ = ΔT₁  512 μs ΔΔT₅ = ΔT₃ + ΔT₄ 1184 μs ΔΔT₆ = ΔT₁ + ΔT₂ + ΔT₃ + ΔT₄2216 μs

The following prediction ratios can be drawn up:

q₁ = ΔΔT₂/ΔΔT₁ = 4 q₂ = ΔΔT₃/ΔΔT₂ = 4 q₃ = ΔΔT₄/ΔΔT₃ = 4 q₄ = ΔΔT₅/ΔΔT₄= 2.3125 q₅ = ΔΔT₆/ΔΔT₅ = 1.8716 . . .

Based upon the above data, the velocity is now established bysuccessively calculating the phase difference for the largest difference(the sum) of the PRI times. The requirement is that the first phasedifference has been clearly determined. This is the case unless thevelocity amount is extremely large. At each stage, firstly the phasechange modulo 2π, xt and then the whole phase change x is calculatedaccording to the following:

 x=(ΔΨ₂−ΔΨ₁)_(mod 2π)  1.

xt=(ΔΨ₃−ΔΨ₁)_(mod 2π)  2.

x=integer((q₁s−xt+π)/2π)·2π+xt

xt=(ΔΨ₄−ΔΨ₁)_(mod 2π)  3.

x=integer((q₂x−xt+π)/2π)·2π+xt

xt=(ΔΨ₁)  4.

x=integer((q₃x−xt+π)/2π)·2π+xt

xt=(ΔΨ₃+ΔΨ₄)_(mod 2π)  5.

x=integer((q₄x−xt+π)/2π)·2π+xt

xt=(ΔΨ₁+ΔΨ₂+Ψ₃+Ψ₄)_(mod 2π)  6.

x=integer((q₅x−xt+π)/2π)·2π+xt

where integer(.) is the integer component of (.). The velocity v is thenobtained by calculating v from the relationship:$v = {\left( {{x/\Delta}\quad \Delta \quad T_{6}} \right) \cdot \frac{{c/2}\quad \pi}{{2\quad \alpha \quad t_{C}} + {2f_{0}}}}$

The radar device 3 shown in FIG. 4, which can be used for realizing theprocess according to the invention, comprises a transmitter part 4 and areceiver part 5. An antenna 6 is connected to the transmitter part andthe receiver part via a circulator 7. The transmitter part includes anoscillator control device 8 coupled to an oscillator 9 having variablefrequency. Frequency sweeps from the oscillator control device 8 controlthe oscillator 9 such that a signal of periodically varying frequency isgenerated having varying period lengths for successive frequency sweeps.The generated signal is sent via a direction coupler 10 and thecirculator 7 out on the antenna 6. The oscillator can operate within theGigahertz range, e.g. 77 GHz. A reflected signal received by the antenna6 is directed via the circulator to a mixer 11, where the reflectedsignal is mixed with the emitted signal. Following amplification in theamplifier 12 and filtering in the filter 13, the signal is fed to aprocessor block 14 in which, inter alia, determination of the relativevelocity is carried out according to the process described above.

The invention shall not in any way be seen to be limited to the exampleabove. Within the scope of the invention defined by the patent claims,there is room for a number of alternative embodiments. For example,other combinations of phase changes can be used.

What is claimed is:
 1. A process for determining a relative velocity ina radial direction between two moving objects, comprising; using linearfrequency modulation with continuous frequency sweeps, wherein atransmitted signal is multiplied by a received signal for the attainmentof a resultant received signal, wherein a phase change of said resultantreceived signal over a time period is used to determine the relativevelocity, wherein a plurality of period lengths associated withsuccessive frequency sweeps are varied, wherein each of a plurality ofsucceeding period lengths is different from each of a plurality ofpreceding period lengths, and wherein a difference in at least one ofthe plurality of period lengths and a corresponding phase change areused to determine the relative velocity.
 2. The process according toclaim 1, wherein the relative velocity v is calculated from therelationship: v=k·x/ΔT, where x is a phase difference during a time ΔT,and${k = \frac{{c/2}\quad \pi}{{2\quad \alpha \quad t_{c}} + {2f_{0}}}},\quad {where}$

c denotes the velocity of light in air, α denotes a gradient of thecontinuous frequency sweep, t_(c) denotes a clock time, and f₀ denotes acarrier frequency of the signal.
 3. The process according to claim 1,wherein a period length from a first to a second frequency sweep ischanged by an amount less than or equal to a time difference necessaryto determine a corresponding phase change based on specified values ofeach of a distance apart, a velocity and an acceleration.
 4. The processaccording to claim 1, wherein at least three successive frequency sweepsare each assigned a different period length.
 5. The process according toclaim 1, wherein any phase changes not resulting from differences inperiod lengths are evaluated to determine the relative velocity usingone or more period lengths.
 6. A method for determining a relativevelocity between two objects, comprising: transmitting a first linearlymodulated signal having a first period length; receiving a first returnsignal reflected from one of said two objects and determining a firstphase change of said first return signal over said first period length;transmitting a second linearly modulated signal having a second periodlength different from said first period length; receiving a secondreturn signal from said one of said two objects and determining a secondphase change of said second return signal over said second periodlength; and calculating the relative velocity using both a differencebetween said first period length and said second period length, and adifference between said first phase change and said second phase change.7. The method of claim 6, wherein said first and said second frequencymodulated signals are linearly modulated signals having a continuousfrequency sweep.
 8. The method of claim 7, wherein said calculating stepincludes calculating the relative velocity v from the relationship:v=k·x/ΔT, where x is a phase difference during a time ΔT, and${k = \frac{{c/2}\quad \pi}{{2\quad \alpha \quad t_{c}} + {2f_{0}}}},\quad {where}$

c denotes the velocity of light in air, α denotes a gradient of thecontinuous frequency sweep, t_(c) denotes a clock time, and f₀ denotes acarrier frequency of the first frequency modulated signal.
 9. The methodof claim 6, further comprising: transmitting a third frequency modulatedsignal having a third period length different from each of the first andsecond period lengths; and receiving a third return signal reflectedfrom one of said two objects and determining a third phase change ofsaid third return signal over said third period length, wherein saidcalculating the relative velocity step also includes using a differencebetween said third period length and said second period length.
 10. Themethod of claim 9, wherein said calculating the relative velocity stepalso includes using a difference between said second phase chance andsaid third phase change.
 11. The method of claim 9, wherein said first,said second, and said third frequency modulated signals are successivelytransmitted.
 12. A method for determining a relative velocity betweentwo objects, comprising: transmitting a plurality of linearly sweptfrequency modulated signals each having a different time periodassociated therewith, wherein each of the plurality of different timeperiods are different from each other; determining a phase change foreach of a plurality of return signals associated with said plurality oflinearly swept frequency modulated signals and reflected from one ofsaid two objects; and calculating the relative velocity between said twoobjects step by evaluating all phase changes not resulting fromdifferences in an associated different time period.